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Phoenix (CNN)That idea that Donald Trump is softening his immigration policy: Not going to happen.

The Republican presidential nominee on Wednesday re-upped the harsh immigration rhetoric that electrified his primary campaign, vowing "no amnesty" for undocumented migrants living in the United States and promising to build a "beautiful" and "impenetrable" border wall that Mexico would pay for -- hours after that country's president vowed that it wouldn't.

"This election is our last chance to secure the border, stop illegal immigration, and reform our laws to make your life better," Trump said in Phoenix at the end of a dizzying day in which he made his first foray into international diplomacy with a visit to Mexico City, then baited a fired-up crowd with red-meat rhetoric.

On what might have been one of the most important days of his presidential campaign, Trump appeared to be recommitting his electoral fate in November to the white conservative base voters who swept him to victory in the GOP primary rather than seeking to broaden his base to a wider coalition of Americans.

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Still, adding to the uncertainty that has clouded his immigration plan in recent days, Trump did not give a definitive answer about what he would do with most of the 11 million undocumented people who are not criminals, leaving open the possibility they would have to continue to hide in the shadows.

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But it was the tone of Trump's speech that was most notable.

"This is it. We won't get another opportunity -- it will be too late," he said in a speech that recreated the vision of a dystopian, crime-riddled nation on the edge of an existential crisis that he deployed in his convention speech in Cleveland in July.

He vowed to create a "deportation task force" within the Immigration and Customs Enforcement division "focused on identifying and quickly removing the most dangerous criminal illegal aliens in America." He said he would boost the ranks of enforcement agents to enforce existing laws. He vowed that any undocumented immigrants who are caught crossing into the US will be "detained until they are removed from our country" and sent back to their country of origin. And he promised to repeal President Barack Obama's executive orders shielding some younger undocumented people, including those born in the United States -- so called Dreamers, from deportation.

Fate of 11 million undocumented immigrants uncertain

Trump left the fate of most of the 11 million undocumented people who are not criminals in the country murky.

He did not commit to deporting every undocumented immigrant living in the US as he previously had, but vowed that immigrants living in the US illegally would never have a path to legal status under his presidency.

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But later, Trump said that once a new immigration system is in place, "we will be in a position to consider the appropriate disposition of those who remain."

In his speech, the billionaire repeatedly called attention to the crimes of some undocumented immigrants and drew on stories of Americans killed by undocumented immigrants, bringing parents of some of those victims on stage to share their graphic and heart-wrenching tales of loss.

Consistent with the law-and-order theme he has emphasized, Trump vowed a "zero tolerance" policy toward criminals living in the US illegally.

As he painted a picture of a country besieged by "illegal alien" crime, Trump accused Washington politicians and the media of underplaying the dangers posed by illegal immigration and warned voters that the stakes this election will never be higher.

"If we can save American lives, American jobs and American futures, together we can save America itself," Trump said.

A quieter Trump in Mexico

Trump's hard-line speech contrasted strikingly with his more moderate tone in Mexico City hours earlier when he put on a restrained and respectful performance, even as he publicly disagreed with President Enrique Peña Nieto, who had invited him and Democratic nominee Hillary Clinton to Mexico for talks.

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The visit was an apparent attempt to portray Trump in a statesmanlike light and to counter Clinton's claims that he is temperamentally unfit to be President. Trump's campaign will likely be pleased that he got a photo-op with a foreign leader and appeared to avoid any damaging gaffes as he stood soberly on stage, beside an interpreter.

But the risks of such a visit -- Trump's first official encounter with a foreign leader -- were underscored when the stagecraft began to unravel over the issue of the wall on the Mexican border.

Trump had told reporters that he and his host did not discuss the cost of who would pay for the multibillion-dollar project -- a statement that the Mexican president did not contest while alongside Trump. But he quickly said on Twitter that the wall came up, and there was no way Mexico would be paying.

"At the start of the conversation with Donald Trump, I made it clear that Mexico will not pay for the wall," Peña Nieto tweeted.

The confusion and apparent contradiction between the two men was quickly seized upon by the Clinton campaign, which mocked Trump, arguing the disconnect undercut his image as a great dealmaker.

"Trump just failed his first foreign test. Diplomacy isn't as easy as it looks. --H" Clinton said in a personally signed Tweet.

Trump just failed his first foreign test. Diplomacy isn't as easy as it looks. -H

Jason Miller, Trump's senior communications adviser, called the meeting "the first part of the discussion and a relationship builder" between the two men.

"It was not a negotiation, and that would have been inappropriate. It is unsurprising that they hold two different views on this issue, and we look forward to continuing the conversation," Miller said in a statement.

Peña Nieto twice stressed the "responsibility" he has to defend Mexican people around the world and said Trump has made "assertions that regrettably had hurt and have affected Mexicans."

"The Mexican people have felt hurt by the comments that have been made. But I am sure that his genuine interest is to build a relationship that will give both of our societies better welfare," Peña Nieto said.

The Clinton campaign also argued that Trump's performance in Mexico proved that his tough guy image was just an act.

"Donald Trump has made his outlandish policy of forcing Mexico to pay for his giant wall the centerpiece of his campaign. But at the first opportunity to make good on his offensive campaign promises, Trump choked," Clinton campaign chairman John Podesta said in a statement.

"What we saw today from a man who claims to be the ultimate 'deal maker' is that he doesn't have the courage to advocate for his campaign promises when he's not in front of a friendly crowd," Podesta said, before accusing Trump of wanting to build a costly wall at American taxpayers' expense.

Podesta later added: "It turns out Trump didn't just choke, he got beat in the room and lied about it."

But Trump was adamant in his speech in Arizona that Mexico would indeed finance the wall if he becomes President.